Biological tissues subjected to rubbing, such as the cornea and eyelid or articular cartilage, are covered in brushy, hydrated mucous structures in order to reduce the shear stress on the tissue. To mimic such biological tissues, we have prepared polyacrylamide (PAAm) hydrogels with various concentrations of un-cross-linked chains on their surfaces by synthesizing them in molds of different surface energies. The selected molding materials included hydrophilic glass, polyoxymethylene (POM), polystyrene (PS), polyethylene (PE), polypropylene (PP), and polytetrafluoroethylene (PTFE). After synthesis, demolding, and equilibration in water, the elastic modulus at the hydrogel surface decreased with increasing water contact angle of the mold. The softer, brushier surfaces did not completely collapse under compressive pressures up to 10 kPa, remaining better hydrated compared to their denser, cross-linked analogs. The hydrogels with brushier surfaces displayed an order of magnitude lower coefficient of friction than the cross-linked ones, which is attributed to the ability of their near-surface regions to retain larger amounts of liquid at the interface. The characteristic speed-dependent friction of the denser, cross-linked hydrogel surface is compared to the speed-independent friction of the brushy hydrogels and discussed from the perspectives of (elasto)hydrodynamic lubrication, permeability, and shear-induced hydrodynamic penetration depth.
Biological tissues subjected to rubbing, such as the cornea and eyelid or articular cartilage, are covered in brushy, hydrated mucous structures in order to reduce the shear stress on the tissue. To mimic such biological tissues, we have prepared polyacrylamide (PAAm) hydrogels with various concentrations of un-cross-linked chains on their surfaces by synthesizing them in molds of different surface energies. The selected molding materials included hydrophilic glass, polyoxymethylene (POM), polystyrene (PS), polyethylene (PE), polypropylene (PP), and polytetrafluoroethylene (PTFE). After synthesis, demolding, and equilibration in water, the elastic modulus at the hydrogel surface decreased with increasing water contact angle of the mold. The softer, brushier surfaces did not completely collapse under compressive pressures up to 10 kPa, remaining better hydrated compared to their denser, cross-linked analogs. The hydrogels with brushier surfaces displayed an order of magnitude lower coefficient of friction than the cross-linked ones, which is attributed to the ability of their near-surface regions to retain larger amounts of liquid at the interface. The characteristic speed-dependent friction of the denser, cross-linked hydrogel surface is compared to the speed-independent friction of the brushy hydrogels and discussed from the perspectives of (elasto)hydrodynamic lubrication, permeability, and shear-induced hydrodynamic penetration depth.
It is known that most
epithelial tissues subjected to rubbing,
such as the cornea and eyelid, or connective tissues, such as articular
cartilage, are covered in brushy, mucous structures in order to reduce
the shear stress on the tissue surface.[1−4] Such protective and lubricative properties
of the mucous structures are attributed to the brushy, gel-like layer
that adheres to the epithelial cells and traps large amounts of water.
Over recent decades, efforts have been made to mimic these effective
biological structures by applying synthetic brush-like layers to various
surfaces to improve their lubrication properties in water. It has
been shown by several studies that surfaces covered with polymer brushes
substantially reduce friction in water compared to bare surfaces.[5−7] Klein et al. have shown that shearing brushes in appropriate solvents
may result in frictional forces that are even below the detection
limit of the surface forces apparatus.[8,9] The interchain
repulsion and incorporation of sufficient quantities of solvent result
in a fluid-filled cushioning layer that can sustain external normal
pressure and reduce shear forces.[10]In contrast to polymeric brushes attached to hard, flat surfaces,
an important property of lubricious biological systems is the presence
of a soft substrate. Corneas, articular cartilage, and other tissues
deform under compressive stress, increasing the contact area and thus
reducing the contact pressure. This helps in keeping the surfaces
hydrated and lubricious. Some synthetic approaches to mimicking such
tissues have involved coating silicone rubber with water-soluble polymer
brushes, which indeed improved frictional properties compared to similar
uncoated substrates.[7,11] However, using hydrogels as substrates
is a step toward actual mimicry of biological, liquid-filled substrates.
Similarly to articular cartilage, for example, hydrogels are soft
and full of interstitial water that can permeate through the structural
network. It has been shown that increasing the amount of water within
the hydrogels and their surfaces reduces interfacial friction.[12,13] However, in order to create supportive substrates with increased
amounts of water at the surface, brush-decorated hydrogels appear
to be a key combination, which has already been successfully used
in the contact-lens industry.[14,15] For example, polyacrylamide
(PAAm) chains grown from within the surface-near region of a denser
polyhydroxyethyl methacrylate (PHEMA) hydrogel was shown to reduce
friction by almost two orders of magnitude.[16]Another way of creating lubricious hydrogels with
a brushy, high-water-content
surface layer is by the inhibition of polymerization close to
the surface during the synthesis of a hydrogel. This can be achieved
by oxygen inhibition as described recently.[17] A straightforward way of creating brushy hydrogels was also introduced
by Gong et al., where a polymer-depleted surface layer is formed during
synthesis close to a hydrophobic molding material.[18,19] They showed, for example, that a poly-2-acrylamido-2-methyl-1-propane-sulfonic
acid (PAMPS) hydrogel synthesized against a Teflon or a polystyrene
(PS) surface has significantly lower friction compared to the same
hydrogel molded against hydrophilic glass.[20] According to their theory and experiments, a homogeneously dense
and cross-linked hydrogel surface is formed close to hydrophilic surfaces
such a glass; however, the thickness of the soft surface layer increases
when more hydrophobic molds are used.[19] Despite the observed correlation between the hydrophobicity, or
rather surface energy, of the molding material and the thickness of
the sparser hydrogel surface, no systematic comparison between the
mold surface energy, hydrogel surface properties, and friction has
been shown.In order to systematically study the link between
the surface properties
of brushy hydrogels and their friction, we have prepared polyacrylamide
hydrogels with different surface properties by synthesizing them against
materials with different surface energies. We have measured water
contact angles and performed infrared (IR) spectroscopy of the molding
surfaces before and after polymerization to check for the presence
of any chemical interactions during the synthesis. Elastic moduli
of the obtained hydrogel surfaces were measured following swelling
and equilibration in water. To check for the ability of the sparse
surfaces to remain hydrated under load, polymer densities near the
surface of different samples under compressive stress were compared
by means of IR spectroscopy. Finally, the coefficient of friction
was measured as a function of sliding speed for the different hydrogel
surfaces sliding against an identical hydrogel surface in water. Self-mated
hydrogels were chosen to bring the experimental conditions closer
to those of an actual biological system. Possible mechanisms for the
substantial differences in friction of different hydrogel surfaces
are presented and discussed.
Materials and Methods
Materials
Acrylamide (AAm, Sigma-Aldrich, St. Louis
MO, U.S.A., > 99%), N,N′-methylenebis(acrylamide)
(bis-AAm, Sigma-Aldrich, > 99.5%), and 2,2′-azobis(2-methylpropionamidine)dihydrochloride
(98%, Acros Organics, New Jersey) were used as monomer, cross-linker,
and initiator, respectively, for the free-radical polymerization reaction.
Milli-Q water was bubbled with nitrogen for 30–45 min in order
to remove the oxygen and then used to dissolve 7.5 wt % of the monomer,
0.3 wt % of the cross-linker, and 0.3 wt % of the initiator by gentle
stirring. The solution was carefully poured into molds to an approximate
thickness of 3 mm. The molds, filled with the solution, were put in
a UV cross-linker (Stratalinker UV Cross-linker 2400, Stratagene Corp.,
La Jolla, CA, U.S.A.) and polymerized for 7 min by a UV light with
an intensity of about 1 mW/cm2 at a wavelength of 365 nm.
After polymerization, the gels were removed from the molds and immersed
in a large amount of Milli-Q water for at least 48 h to remove unreacted
species and allow swelling of the gels.The materials of the
molding surfaces were glass, polyoxymethylene (POM, Kern GmbH, Germany),
polystyrene (PS, TPP Techno Plastic Products AG, Switzerland), polyethylene
(PE, common low-density PE zip-loc bag, Minigrip, Alpharetta, GA,
U.S.A.), polypropylene (PP, Entegris Inc., Billerica, MA, U.S.A.),
and polytetrafluoroethylene (PTFE, Kern GmbH, Germany). For the glass
and the PS mold, common glass and PS Petri dishes were used, respectively.
The other materials (POM, PE, PP, and PTFE) were obtained as thin
sheets that were glued into a PS Petri dish. All the molding materials
were rinsed and sonicated for 10 min in isopropanol prior to use.
Chemical structures and water contact angles of the selected materials
are presented in Table .
Table 1
List of Molding Materials with Their
Abbreviations, Chemical Structures, Water Contact Angles, Surface
Tensions, and Surface Roughnessesa
Presented
surface-roughness values
are averaged values obtained by atomic force microscopy in tapping
mode and by optical profilometry (see Supporting Information).
Presented
surface-roughness values
are averaged values obtained by atomic force microscopy in tapping
mode and by optical profilometry (see Supporting Information).
Contact Angle
In order to check the initial state and
any polymerization-induced degradation of the molds, the static water
contact angles with the mold surfaces were measured with a NRL CA
goniometer (model 100–00–230, Rame-Hart Inc., NJ, U.S.A.)
before and after the polymerization. Before the contact-angle measurements,
the molds were sonicated in isopropanol for 10 min. The contact angle
was measured on both sides of the droplet on at least five different
locations of the mold surface. The contact angle of glass was too
low to be measured and was therefore assumed to be less than 5 degrees
before and after the polymerization. All measurements were performed
at a room temperature of 22 ± 1 °C.
Infrared Spectroscopy
In order to further verify the
initial state of the molds and possible polymerization-induced degradation,
attenuated-total-reflection Fourier-transform infrared (ATR-FTIR)
spectroscopy of the mold surfaces was performed. The measurements
were carried out with the Alpha-P ATR-IR (Bruker, Billerica, MA, U.S.A.),
equipped with a diamond ATR crystal and a DTGS detector. The spectra
were recorded from 500 to 4000 cm–1 with 64 scans
at a resolution of 4 cm–1 for each sample.ATR-IR spectra were also recorded for the surfaces of hydrogels molded
against different molds as shown in Figure . Round discs of 10 mm diameter were punched
out of 4–5 mm thick hydrogel slabs and attached to 10 mm flat-ended
steel pins using a thin layer of cyanoacrylate-based superglue (Pattex,
Henkel AG & Co. KGaA, Düsseldorf, Germany). The pins with
the gels were then pressed with the side of interest against the diamond
ATR crystal using the normal loads of 0.1, 0.5, and 1 N, which corresponds
to contact pressures in the range of 1 to 14 kPa. Before each measurement,
the ATR crystal was cleaned with isopropanol and the background was
recorded in pure Milli-Q water. The measurements were repeated three
times at each condition and then averaged.
Figure 1
Schematic of ATR-IR experiments
with hydrogels showing a flat hydrogel
disc attached to a flat stainless-steel pin and pressed against a
diamond ATR crystal at various loads. The intensity of the characteristic
peaks in the IR spectrum depends on the polymer density close to the
hydrogel surface and the applied load.
Schematic of ATR-IR experiments
with hydrogels showing a flat hydrogel
disc attached to a flat stainless-steel pin and pressed against a
diamond ATR crystal at various loads. The intensity of the characteristic
peaks in the IR spectrum depends on the polymer density close to the
hydrogel surface and the applied load.
Nanoindentation
Nanoindentation experiments were performed
on hydrogel surfaces that were molded against the selected molds,
using an atomic force microscope (AFM, MFP-3D, Asylum Research, Santa
Barbara, U.S.A.). The Sader method was applied to determine the normal
spring constant (k = 1.57 N/m) of the gold-coated
tipless cantilever (NSC-36, Mikromash, Estonia).[22] A silica microsphere (GP0083, Whitehouse Scientic, Waverton,
UK) with a radius of 11 μm was glued to the end of the tipless
cantilever with a 2-component epoxy resin adhesive (UHU GmbH, Germany)
by means of a home-built micromanipulator. The spring constant was
then corrected for the colloid position on the cantilever as k′ = k (L′/L)[3] = 1.98 N/m, where L is the cantilever length and L′
is the distance from the base of the cantilever to the colloid position.[23] Indentation speed was set to 1 μm/s, which
was slow enough to avoid significant contributions from the visco-
or poro-elasticity of the hydrogel samples. The very minor hysteresis
between the approach and retraction parts of the indentation reflects
the insignificance of such contributions. All measurements were performed
at room temperature of 22 °C ± 1 °C with samples completely
immersed in milli-Q water in order to minimize any capillary forces
between the probe and the investigated surfaces. Prior to the measurements,
the optical-lever sensitivity S was calibrated by
pressing the probe against a hard surface of a silicon wafer in water
to obtain the relation between the cantilever deflection and the photodiode
signal. An acquisition rate of 2000 Hz was used. Force maps of 3 ×
4 force curves were obtained over an area of 40 × 40 mm2 at three different locations on a sample.For the data analysis,
the background slope and the offset that were calculated for the signal
away from the surface were subtracted from the entire curve. The root-mean-square
value of the noise away from the surface was determined to be σ
≈ 50 pN. The exact contact point was therefore determined on
the approach curve as the last data point lying within 2σ from
the zero-force line. The indentation depth was calculated as d = Z - ∂ = Z – SU, where Z is the measured piezo position, ∂
is the cantilever deflection, S is the optical sensitivity,
and U is the measured photodiode signal. The force
was calculated as F = k ∂,
and the results are presented as force–indentation (F-d) curves.
Friction
The coefficient of sliding
friction of the
gels was measured using a tribometer (CSM, Needham, MA, U.S.A.) in
reciprocating configuration. The schematic of the friction experiments
is shown in Figure . Similarly to the FTIR experiments, flat discs of 10 mm diameter
were punched out of 4–5 mm-thick hydrogel slabs and glued to
flat-ended steel pins of the same diameter. The pin with the hydrogel
was pressed against the surface of a larger slab of a similar hydrogel
that was glued into a polystyrene Petri dish. In this way, the hydrogel
surfaces that were synthesized against the same molding surface were
brought into contact. The normal load was set to 0.5 N, which corresponds
to a contact pressure of about 6 kPa and is close to the range of
contact pressures that occur between an eyelid and a cornea during
a blink of an eye.[24] The stroke length
was set to 10 mm, and sliding speeds were varied from 0.1–15
mm/s. The tests consisted of 10–20 cycles at each condition,
which was sufficient for the friction force to reach a steady state.
The friction coefficient μ was defined as the friction force
divided by the normal load and was determined for each cycle from
the middle 20% of the stroke length. The friction loops appeared symmetrical,
indicating only negligible transient effects upon reversal of the
sliding motion (Figure S3 in Supporting Information). The average friction
coefficient was calculated over the last 5 cycles. The tests were
performed at 22 °C ± 1 °C with samples fully immersed
in pure milli-Q water.
Figure 2
Schematic of the friction experiments, where a flat hydrogel
pin
of 10 mm in diameter was sliding reciprocally over a larger flat piece
of a hydrogel with a matching surface. The normal load was 0.5 N (6
kPa) and the range of sliding speeds was 0.1–15 mm/s in the
middle of the stroke.
Schematic of the friction experiments, where a flat hydrogel
pin
of 10 mm in diameter was sliding reciprocally over a larger flat piece
of a hydrogel with a matching surface. The normal load was 0.5 N (6
kPa) and the range of sliding speeds was 0.1–15 mm/s in the
middle of the stroke.
Results and Discussion
Contact
Angle
Figure shows water contact angles of the molding surfaces
according to the literature[21] as well as
before and after the polymerization of the gels. The obtained contact
angles before the polymerization agreed with the literature data,
confirming the chemical structures and cleanliness of the molding
surfaces in this work. The water contact angles also did not change
significantly after the free-radical polymerization of the gels in
the molds, which indicates that no significant chemical interaction
with the mold occurred during the polymerization. Similar observations
were also made by Gong et al.,[18,19] who proposed that the
heterogeneous polymerization at the surface occurs due to the differences
in surface tension of the polymerizing solution and the molding surface.
According to Gong et al., the surface-tension difference increases
during the polymerization. Due to the higher surface tension
of the polymer solution compared to the monomer solution, the entangled
polymer network is pushed away from the surface by osmotic pressure
and replaced by a monomer-depleted solution close to the surface in
order to decrease the Gibbs free energy of the system. This causes
a formation of a loose polymer network close to the surface without
any chemical interactions with the molding surface itself. Our results
cannot confirm Gong’s proposed mechanism, although they are
consistent with the absence of chemical interaction and show that
the molds can be reused after the polymerization process.
Figure 3
Water contact
angles of the mold materials according to the literature,[21] before the polymerization and after the polymerization
of the hydrogels.
Water contact
angles of the mold materials according to the literature,[21] before the polymerization and after the polymerization
of the hydrogels.To further verify the absence
of chemical interactions of the polymerizing solution with the molds,
ATR-IR spectra of the molding surfaces were recorded before and after
the polymerization. Figure shows the corresponding spectra for all the polymeric molds.
The obtained spectra match the expected spectra of the used molds
and show no significant changes following polymerization of the hydrogels.
The results agree with those of the water-contact-angle analysis presented
above.
Figure 4
ATR-IR spectra of mold surfaces before and after hydrogel polymerization.
No changes were observed in the surface composition due to free-radical
polymerization.
ATR-IR spectra of mold surfaces before and after hydrogel polymerization.
No changes were observed in the surface composition due to free-radical
polymerization.Figure a shows
a characteristic transmission IR spectrum of a glass-molded PAAm hydrogel
surface pressed against an ATR-IR crystal with a pressure of about
8 kPa. Since pure water was used for the background spectrum, the
broad peak that corresponds to the water O–H stretch at 3700–3000
cm–1 should appear above 100% transmission due to
the lower amount of water within the hydrogel compared to pure water.
However, the peak is superimposed with symmetric and asymmetric N–H
stretching vibrations of the acrylamide in the same region. More intense
peaks appear in the C=O stretching region, with the amide I band at
about 1660 cm–1 and the amide II band at about 1610
cm–1 (N–H bend) being the most pronounced
(Figure b).
Figure 5
Example of
an ATR-IR spectrum of a glass-molded hydrogel surface
pressed against the ATR-IR crystal with a contact pressure of 8 kPa.
(a) Entire spectral range. (b) Region between 1800 and 1250 cm–1.
Example of
an ATR-IR spectrum of a glass-molded hydrogel surface
pressed against the ATR-IR crystal with a contact pressure of 8 kPa.
(a) Entire spectral range. (b) Region between 1800 and 1250 cm–1.In order to evaluate
the selected peak intensities obtained from
different samples and at different contact pressures, the amide I
and amide II bands were deconvoluted using a linear combination of
Gaussian and Lorentzian functions. The integrated area of the deconvoluted
amide II (N–H bending) band positioned at 1610 cm–1 is presented for variously molded gels as a function of contact
pressure in Figure . The results for amide I (C=O) band were qualitatively similar and
only differed in their peak intensities. Peak intensities correspond
to the amount of polymer concentration within the first few microns
of a hydrogel surface. Therefore, the higher the intensity, the denser
the polymer network at the hydrogel surface. As expected from the
theory of heterogeneous polymerization presented by Gong, the hydrogel
molded against the most hydrophilic (glass) mold showed the highest
polymer concentration at the surface. All the other more hydrophobically
molded hydrogels had much sparser polymer networks at the surface.
Small differences in water contact angles (surface tensions) of the
hydrophobic, polymeric molds resulted in rather small differences
in hydrogel polymer densities. However, hydrogel surface polymer density
tended to decrease with decreasing surface tension of the mold. For
example, POM with its relatively high surface tension yielded a denser
hydrogel surface compared to the more hydrophobic molds such as PP
or PTFE.
Figure 6
Averaged peak intensities from ATR-IR spectra of variously molded
gels pressed against the ATR-IR crystal with different contact pressures.
Averaged peak intensities from ATR-IR spectra of variously molded
gels pressed against the ATR-IR crystal with different contact pressures.Increasing the contact pressure from less than
2 kPa to more than
13 kPa resulted in an increase in peak intensities and thus hydrogel
polymer density in all the cases, which is due to the compression
of the hydrogels and migration of water from the surface region. Therefore,
all the hydrogel surfaces were observed to densify upon compression.
Interestingly, however, none of the hydrogel surfaces showed a complete
exudation of water from the surface region even at the highest applied
contact pressure. In the case of complete dehydration, the intensity
of the peaks corresponding to the PAAm polymer would have increased
well above the intensities observed for the glass-molded gel, which
are assumed to represent the bulk of an equilibrated, swollen gel.
This means that the affinity to water was sufficient to keep even
the sparsest hydrogel surfaces relatively well hydrated at these contact
pressures. Therefore, even at increased contact pressures, the water
content was higher for the gels that were molded against more hydrophobic
molds. This is an important finding also for the tribological tests
that were performed at a contact pressure of about 6 kPa, which is
close to the middle of the contact-pressure range used in the ATR-IR
experiments.Figure a shows force–distance
curves obtained during
the colloidal-probe nanoindentation of variously molded hydrogel surfaces
in water. The glass-molded gel showed the stiffest response with the
shape of the force–distance curve following Hertzian contact
mechanics, indicating a homogeneous structure right from the surface.
The other hydrogels showed much softer response at the initial indentation
that then gradually stiffened with increasing indentation. The shaded
area in Figure a depicts
the range of indentation depths within the first 2 μm that was
used for the analysis of the elastic modulus. Hertzian contact mechanics
were used to fit the indentation part of the force–distance
curves in that range, and the obtained elastic moduli are shown in Figure b as a function of
the mold contact angle. The glass-molded sample had the highest elastic
modulus. For the hydrogels molded in more hydrophobic molds, the elastic
modulus at the surface decreased with increasing contact angle (decreasing
surface tension) of the molds. The obtained elastic moduli of the
hydrogel surfaces produced in molds with water contact angles above
87° or surface tension below 34 mN/m were below 1 kPa and therefore
more difficult to differentiate. However, looking at the force–distance
curves and comparing indentation depths at a certain force, it appears
that the thickness of the soft top layer increased with decreasing
mold surface tension. The only exception seems to be the PS mold,
which, despite having a surface tension that falls in the middle of
all the molds used, yielded the softest and likely also the thickest
hydrogel surface layer. Since the Hertzian fit to the data is an integrated
value over a gradient of properties, the low elastic modulus in this
case could be due to a different shape of the density gradient of
the PS-mold hydrogel surface. The molds had indeed substantially different
surface roughness values, which could affect the surface of the hydrogels
to some extent. One could assume that increasing the surface roughness
of a mold would increase the surface roughness of a hydrogel, thus
making it appear softer upon indentation. In our case, however, the
glass and PS molds had the lowest and comparable roughness values
but yielded hydrogels with the most different surface moduli. Besides,
the PS mold was substantially smoother than any other polymeric mold
in this work and still yielded the softest hydrogel surface. Moreover,
the elastic moduli were determined from a depth range that greatly
exceeds the surface roughness values. Therefore, mold surface roughness
should have only a negligible effect on the surface modulus of the
hydrogels and we believe the surface chemistry is the dominant parameter
affecting hydrogel surfaces in our case.
Figure 7
(a) Representative force–distance
curves obtained by colloidal-probe
nanoindentation of variously molded hydrogel surfaces in water. The
shaded area depicts the range of indentation depths used for fitting
the Hertzian model and extraction of elastic modulus. (b) Average
elastic modulus within the first 2 μm of hydrogel surfaces as
a function of water contact angle of the respective molding surfaces.
The dashed line is a guide for the eye.
(a) Representative force–distance
curves obtained by colloidal-probe
nanoindentation of variously molded hydrogel surfaces in water. The
shaded area depicts the range of indentation depths used for fitting
the Hertzian model and extraction of elastic modulus. (b) Average
elastic modulus within the first 2 μm of hydrogel surfaces as
a function of water contact angle of the respective molding surfaces.
The dashed line is a guide for the eye.Figure shows the coefficient of friction as a function of sliding
speed for variously molded hydrogel surfaces sliding against an identical
hydrogel surface in a flat-pin-on-disc configuration. Figure b is a full logarithmic plot
of Figure a to highlight
the speed-dependent scaling of friction and for reasons of clarity
in the low-friction regime.
Figure 8
Coefficient of friction μ of self-mated
hydrogels as a function
of sliding speed. (a) Semilogarithmic plot. (b) Logarithmic plot.
Coefficient of friction μ of self-mated
hydrogels as a function
of sliding speed. (a) Semilogarithmic plot. (b) Logarithmic plot.Glass-molded hydrogel surfaces displayed the highest
friction over
the whole range of sliding speeds ranging from relatively low values
of ∼0.06–0.08 at low sliding speeds to over 0.5 at the
highest sliding speed. The speed-dependent friction increase scaled
with sliding speed to the power of 1/2 (Figure b). Similar speed-dependent behavior was
also observed in other recently published papers.[12,25−28] According to Urueña et al., soft elasto-hydrodynamic (EHL)
lubrication theory could not explain the friction data, since the
friction coefficient predicted by the theory falls significantly below
the measured values.[12,29] The authors state that the viscoelastic
nature of the polymer network and the non-Newtonian behavior of water
at the shearing interface could play a role; however, their contributions
could not be resolved.[12,30]Assuming purely hydrodynamic
lubrication with the friction force
being F = AηU/h, where A is contact area, η is the dynamic viscosity, U is the sliding speed, and h is water
film thickness, this would in our case, for a coefficient of friction
of 0.45 at the sliding speed of 10 mm/s, yield a film thickness of
about 3–4 nm. The value indeed seems low but still reasonable.
According to de Gennes, the mean hydrodynamic film thickness should
scale with sliding speed as h ∝ U0.5.[31] The above equation
would thus yield a coefficient of friction that scales as μ
∝ U0.5, as also observed in this
work.The isoviscous-elastic case of the soft EHL theory, developed
by
Hamrock and Dowson, returns film thicknesses in the order of hundreds
of nanometers and thus friction coefficient values that are significantly
below our measured values, as also observed by Urueña et al.[12] According to the soft EHL theory, the film thickness
should scale with sliding velocity as h ∝ U0.65.[32] Considering
this relationship, the coefficient of friction would then scale with
speed as μ ∝ U0.35. This
is indeed less than the observed power of 1/2; however, the difference
could also come from the viscoelastic and/or poro-elastic dissipation
of the migrating deformation.[33−35] Poroelastic flow due to deformation
could also contribute to the speed-dependent friction increase for
the hydrogel with the denser surface structure. However, for the different
surface layers, as in our case, the exact contributions of the mentioned
dissipation phenomena remain unclear.Two POM-molded hydrogels
in contact, however, had in general lower
friction than the glass-molded hydrogels. At the same time, the friction
showed a smaller increase with increasing sliding speed (i.e., μ
∝ U; n ∼ 0.33) compared to the glass-molded gel (Figure ). The lower friction
could be explained by the lower amount of polymer in contact compared
to the case of the glass-molded hydrogel, as shown in Figure . The sparser surface of the
POM-molded hydrogel, and thus the larger pore size, could allow for
an enhanced poroelastic diffusion of water close to the surface driven
by the interfacial shear. Such hydrodynamic penetration depth would
effectively increase the region of “interfacial” shearing
of water h, i.e., which could reduce the shear rate
( = U/h) and thus the shear
stress (τ = η). A speed-dependent
increase in shear could
cause the hydrodynamic penetration depth to increase with sliding
speed, which would result in a friction coefficient with a lower degree
of speed dependency (μ ∝ U; n < 1/2) compared to the glass-molded
case.All the other hydrogel surfaces that were molded against
more hydrophobic
molds (i.e., PS, PE, PP, PTFE) showed even lower coefficients of friction,
which were in the range of ∼0.01–0.05. The friction
of all these hydrophobically molded hydrogels was almost independent
of the sliding speed. Considering the even sparser surface structures
of these gels compared to the glass- and POM-molded hydrogels, the
shear-induced increase of the hydrodynamic penetration depth could
be almost linearly proportional to the sliding speed h ∝ f(U) ∼ U, which would yield a more speed-independent coefficient
of friction μ ∝ U/h ∼ U0.According to these results, hydrogels with a dense, cross-linked
surface appear to behave like an impermeable body, resulting in a
speed-dependent friction increase that follows the common (elasto)hydrodynamic
theory (Figure ).
Sparser, brushy hydrogel surfaces may allow shear-driven diffusion
within the soft surface layer, increasing the hydrodynamic penetration
depth and thus reducing the speed dependency of the friction coefficient.
However, in order to better verify these statements, further experiments
are needed.
Figure 9
Possible mechanisms for speed-dependent friction in the case of
dense hydrogel surfaces (left) and for speed-independent friction
in the case of hydrogels with sparser surface layers (right).
Possible mechanisms for speed-dependent friction in the case of
dense hydrogel surfaces (left) and for speed-independent friction
in the case of hydrogels with sparser surface layers (right).
Conclusions
PAAm hydrogels have
been synthesized by free-radical polymerization
in molds of various surface energies, ranging from hydrophilic to
hydrophobic. We have confirmed that the mold material indeed
affects the surface of a hydrogel. This appears to occur in the absence
of a chemical interaction that would alter the structure of the mold.
Hydrophilic molds such as glass resulted in the densest surface structure
of a hydrogel, whereas the hydrogel surfaces became softer and sparser
with the use of more hydrophobic molds such as PS, PE, PP, and PTFE.
Although the elastic modulus at the hydrogel surface in principle
decreased with increasing hydrophobicity of the molds, the water contact
angle and thus the surface tension or the surface energy seem not
to be the only important parameters. We have also shown that
sparser and presumably brushier hydrogel surfaces do become compressed
but do not collapse completely under contact pressures up to 10 kPa.
Below this contact pressure, the polymer density near the surface
of the brushy hydrogel remains lower compared to that near the densest,
glass-molded hydrogel surface. Such different hydrogel surfaces also
present different frictional behaviors during sliding against matching
surfaces at nominal contact pressures of about 6 kPa in water. The
densest, glass-molded hydrogel surfaces showed the highest coefficients
of friction, which increased with sliding speed to the power of 1/2.
Sliding sparser, brushier hydrogel surfaces reduced the friction and
progressively decreased the speed dependency. While the polymer density
in a sliding contact might affect the friction at low sliding speeds,
the fluid-film formation presumably dictates the friction at higher
sliding speeds. The friction behavior of the dense, glass-molded hydrogel
surface could be explained in terms of the (elasto)hydrodynamic lubrication
theory, assuming impermeable surfaces. The decrease in speed dependency
with decreasing surface polymer density could be a consequence of
the progressively increasing hydrodynamic penetration depth within
the sparser surface.
Authors: Tooba Shoaib; Joerg Heintz; Josue A Lopez-Berganza; Raymundo Muro-Barrios; Simon A Egner; Rosa M Espinosa-Marzal Journal: Langmuir Date: 2017-10-17 Impact factor: 3.882
Authors: Nicholas L Cuccia; Suraj Pothineni; Brady Wu; Joshua Méndez Harper; Justin C Burton Journal: Proc Natl Acad Sci U S A Date: 2020-05-12 Impact factor: 11.205
Authors: Kaihuan Zhang; Wenqing Yan; Rok Simic; Edmondo M Benetti; Nicholas D Spencer Journal: ACS Appl Mater Interfaces Date: 2020-01-24 Impact factor: 9.229